What can we learn by comparing experimental and theoretical-computational X-ray scattering data?

doi:10.1016/j.molliq.2008.07.012

Journal of Molecular Liquids

Volume 144, Issues 1–2, 10 January 2009, Pages 9-12

https://doi.org/10.1016/j.molliq.2008.07.012 Get rights and content

Abstract

In this letter we use X-ray scattering data of liquid water, as obtained by different experimental and theoretical-computational procedures, to address the problem of quantitative modeling of the scattering signal in liquids. In particular we investigate the accuracy of well optimized water models in reproducing top level X-ray experimental results and compare experimental data variations with the ones given by different theoretical-computational models. Results show that the experimental scattering data have an intrinsic noise which is comparable to the deviations of the theoretical-computational signals, hence suggesting that no reliable refinement based on scattering data is possible for such models.

Introduction

The structure of liquid water has been the research subject of a lot of theoretical and experimental groups worldwide, for thirty years. The pioneering study of Narten and Levy [1], is commonly considered as providing a reliable and accurate description of X-ray diffraction of liquid water at room temperature, to be compared to related theoretical studies [2], [3], [4], [5]. G. Hura et al. [6] performed a new X-ray diffraction study of liquid water under ambient conditions, which was subsequently [7], [8] used, in conjunction with theoretical-computational data, to address the problem of modelling X-ray scattering data by a molecular simulation in order to obtain an accurate radial distribution function. In one of these articles [7] the authors state that the differences seen between their X-ray intensity profile and previously reported scattering curves (essentially the paper of Narten and Levy [1]) are significant, and hence utilize the detailed information of their scattering profile to obtain (empirically) new atomic scattering factors and select optimal water molecular models. Because of the discrepancy among the experimental results of such studies and the possible relevance for molecular modelling of X-ray data, we decided to accomplish new measurements with our EDXD (Energy Dispersive X-ray) diffractometer, which has proven to be particularly suited to study liquid and amorphous samples [9], [10], [11], [12], [13], [14], [15], [16], [17], to perform a detailed comparison with scattering data obtained by simulations and address the problem of evaluating the optimal water model and/or atomic scattering factors to be used in molecular simulations of X-ray scattering signal.

Section snippets

Theory

The scattering intensity for a given atomic configuration is defined by I(S) = |F(S)|² where the structure factor F(S) due to a set of n atoms within a volume V is [18], [19] $F (S) = \sum_{j = 1}^{n} f_{j} (S) e^{2 π i S \cdot r_{j}}$ with r_j the position vector of the jth atom, S the scattering vector, S = |S|, f_j(S) the jth atom scattering factor and $i = \sqrt{- 1}$ . Therefore the observed scattering intensity, corresponding to the intensity averaged by the atomic configurational distribution, may be written as $\begin{array}{l} 〈 I (S) 〉 = 〈 \sum_{j = 1}^{n} \sum_{k = 1}^{n} f_{j} (S) f_{k} (S) e^{2 π i S \cdot (} \end{array}$

Methods

We performed our experiments using the non-commercial energy-scanning diffractometer built in the Department of Chemistry of the University of Rome La Sapienza. Detailed description of both instrument and technique can be found elsewhere [11], [15]. Transmission geometry has been employed and the white Bremsstrahlung component of the radiation emitted by a tungsten tube working at 50 kV and 40 mA was used. Scattered intensities for the samples and for the empty cell were measured at seven

Results

In Fig. 1 we compare our experimental scattering data with data published in previous papers [1], [6]. The figure clearly shows that the three experimental data sets are very close in the right tail and present larger deviations in the principle peak region. Such data variations may be quantitatively expressed by the root mean square relative deviations (RMSRD) reported in Table 1, indicating moderate but not negligible variations. Interestingly, our experimental scattering profile is closer to

Conclusions

In this letter we compared three experimental scattering data sets with three different theoretical scattering signals, as obtained by MD simulations of SPCE and SPC water models using either the usual atomic scattering factors or the modified atomic scattering factors (MASF) of Hura et al.. Results indicate that the variations of the theoretical data, as provided by the use of these related but different water models and/or the inclusion of MASF, are roughly comparable to the differences of

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It has been considered to be a suitable tool for the investigation of liquid systems because of its high speed and good reliability compared with a traditional angular scanning diffractometer [1,2,14–17]. Recently, intermolecular structure of pure liquid and solution has already been investigated extensively at different conditions by means of EDXRS in order to study the local structure of H-bonding, hydration and molecular aggregation [17–22]. Liquid materials such as hazardous liquid fuel, liquid explosives and precursor chemicals are deserved special attention by security screening.
Application of the energy dispersive X-ray scattering (EDXRS) for the identification of pure liquid materials was reported for the first time. Three liquid systems of primary alcohols, benzene homologues and chloromethanes were carefully probed and the scattering spectra were described. On the basis of the different structures and compositions of these compounds, the scattering profiles of all media exhibit characteristic shapes, which implies that the EDXRS profile is unique to the specific material and significant differences of profiles amongst various liquid substances can be observed. Moreover, the result suggests that non-invasive EDXRS approach would be quite promising in the field of liquid discrimination/recognition.
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What can we learn by comparing experimental and theoretical-computational X-ray scattering data?

Abstract

Introduction

Section snippets

Theory

Methods

Results

Conclusions

Chem. Phys.

Comp. Mat. Sci.

Chem. Phys. Lett.

J. Chem. Phys.

J. Chem. Phys.

J. Chem. Phys.

J. Chem Phys.

Phys.

J. Chem. Phys.

Phys. Chem. Chem. Phys.

Inorg. Chem.

J. Mater. Chem.